This is another problem from BL’s Math Games.

“What fraction of the rectangle is colored?  Assume that M and N are midpoints of the sides of the rectangle.”

That they are midpoints was not stated explicitly in the problem as given in front of the subscription wall, but from the comments it became evident this was the case.

Initially I actually assumed the line was positioned arbitrarily.  What would be the solution in that case?

Answer to BL problem.

See ZigZag in Rectangle for a solution.